Starting or changing the depth of the face cut; changes front face position of mechanically the most key central pivot, benchmark to measure everything in terms of distance/angle from. Unless backlean, then is a key receiver not an initial position.
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Treat as tree is weightless rigid form, and all weight force is cannonball as CoG within tree form boundary.
The loaded angle from the CoG to compression pivot point(benchmark) in the hinge as most rigid point closest to CoG(most efficient, available support position taken by smartest player Nature). Then the side2side and front to back amount of extreme geometries and their length/angle available within the hinge patch from that key central pivot just given against the CoG on the other side of central pivot as benchmark. Also how much the total force forward is concentrated or spread across to the length of the front face it folds on as greatest points to me.
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On close the leveraged length of the faces close slapping and side pressures to CoG would give some effects too, as well as side2side closes. Especially if working L/R sides of the faces independently(Step-Dutch forms) type strategy analogous to not working the L/R face sides generically/same, just as don't work backfield the same in Tapered Hinge L/R sides.
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To be confident all of this to react cleanly as calc'd; requires the thing to be kept to monolith of no separate internal moving 'plates' to bind against each other to seize or change the formula as the motion plays out; so have 1 single committed clean motion with extreme hinge and face positions as only competitors to the CoG motion x angle x leveraged distance.
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In building hinge, we speak of what we take, but it is what we leave behind that matters. The thing is already not going where ya don't want it to go as is, want to mimic/exploit those positions i think. Tapered Hinge more follows the stress pattern already there in stump, now just not removed in hinge etc. from getting 'too happy' w/saw, cutting too much. To start on this chessboard, that might require moves at times beyond checkers.